I'm currently studying a chapter on Differentiation. I was introduced to first prinicples, and i found a few of the first questions easy. But, ive hit a dead end, and nothing I try with this next question works. I looked up the method and found explanations at:

First Principles

However, this does not help me get the answer I seek. Could you please help?

The question goes:

"Use First principles to find $\displaystyle dy/dx$

$\displaystyle y=6x-2x^2$

Now i used the formula, and got something like this:

$\displaystyle \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

$\displaystyle = \lim_{h \rightarrow 0} \frac{6(x+h)-2(x+h)^2-(6x-2x^2)}{h}$

From here, I have no idea, Ive tried many different ways and I always end up with the wrong answer.

Please explain to me how to do this.